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Non-darcy buoyancy flowin a square cavity filled with porous medium for various temperature difference aspect ratios
Published in
2011
Volume: 14
   
Issue: 7
Pages: 649 - 657
Abstract
A finite element analysis has been carried out to study the influence of a sinusoidally heated bottom wall and linearly heated side walls on natural convection flows in a square cavity filled with a porous medium when the top wall is well insulated. The Darcy-Forchheimer model without the inertia term is used to predict the temperature and flow circulations in the porous medium. In the present study, for a non-uniformly heated bottom wall, the maximum temperature TH was attained at the center of the bottom wall. The side walls were linearly heated, maintaining minimum temperature Tc at the top edges of the side walls and temperature Th at the bottom edges of the side walls; i.e, Tc ≤ Th ≤ TH. The penalty finite-element method with bi-quadratic rectangular elements was used to solve the non-dimensional governing equations for coupled thermal and flow fields. Numerical results are presented for a wide range of parameters of temperature difference aspect ratio A = (Th - Tc)=(TH - Tc)(0 ≤ A ≤ 1) and Darcy number Da (10-5 ≤ Da ≤ 10-3) for higher Rayleigh number Ra = 106 and Prandtl number Pr = 0:7 in terms of stream functions and isotherm contours. Furthermore, the effect of the temperature difference aspect ratio on local and average Nusselt numbers has been analyzed. © 2011 by Begell House, Inc.
About the journal
JournalJournal of Porous Media
ISSN1091028X
Open AccessNo
Concepts (22)
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    BOTTOM WALL
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    DARCY NUMBER
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    FLOW CIRCULATION
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    Governing equations
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    LINEARLY HEATED SIDE WALLS
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    Maximum temperature
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    Natural convection flow
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    NONUNIFORM HEATING
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    Numerical results
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    Porous medium
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    Rayleigh number
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    SIDE WALLS
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    Square cavity
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    Streamfunctions
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    TEMPERATURE DIFFERENCE ASPECT RATIO
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    Temperature differences
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    Finite element method
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    Natural convection
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    Nusselt number
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    Porous materials
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    Wall flow
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    Aspect ratio